Problem of the Week

Updated at Aug 23, 2021 5:59 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve x25(5−5x)=6\frac{{x}^{2}}{5}(5-\frac{5}{x})=6?

Check out the solution below!



x25(5−5x)=6\frac{{x}^{2}}{5}(5-\frac{5}{x})=6

1
Use this rule: ab×c=acb\frac{a}{b} \times c=\frac{ac}{b}.
x2(5−5x)5=6\frac{{x}^{2}(5-\frac{5}{x})}{5}=6

2
Factor out the common term 55.
x2×5(1−1x)5=6\frac{{x}^{2}\times 5(1-\frac{1}{x})}{5}=6

3
Regroup terms.
5x2(1−1x)5=6\frac{5{x}^{2}(1-\frac{1}{x})}{5}=6

4
Cancel 55.
x2(1−1x)=6{x}^{2}(1-\frac{1}{x})=6

5
Expand.
x2−x=6{x}^{2}-x=6

6
Move all terms to one side.
x2−x−6=0{x}^{2}-x-6=0

7
Factor x2−x−6{x}^{2}-x-6.
(x−3)(x+2)=0(x-3)(x+2)=0

8
Solve for xx.
x=3,−2x=3,-2

Done
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